Question

the fairness of a particular coin is being investigated by flipping the coin. which of the following experiment results provide the most evidence that the coin is not fair?
o a 1 out of 500 flips is a head
o b 1 out of 50,000 flips is a head
o c 5 out of 5,000 flips are heads
o d 50 out of 500 flips are heads
o e 500 out of 5,000 flips are heads

Explanation:

Step1: Calculate the probability of each option

For a fair coin, the probability of getting a head \(P(H)=\frac{1}{2} = 0.5\)

• Option A: Probability \(P_A=\frac{1}{500}=0.002\)
• Option B: Probability \(P_B=\frac{1}{50000}=0.00002\)
• Option C: Probability \(P_C=\frac{5}{5000}=\frac{1}{1000}=0.001\)
• Option D: Probability \(P_D=\frac{50}{500}=\frac{1}{10}=0.1\)
• Option E: Probability \(P_E=\frac{500}{1000}=0.5\)

Step2: Compare with the fair - coin probability

The probability of a fair coin getting a head is \(0.5\). The option with the probability farthest from \(0.5\) is the most indicative that the coin is not fair.

Among \(P_A = 0.002\), \(P_B=0.00002\), \(P_C = 0.001\), \(P_D=0.1\) and \(P_E = 0.5\), \(P_B\) is the smallest.

Answer:

B. 1 out of 50,000 flips is a head